The quantum field theoretic anomalies are in four dimensions defined by triangle diagrams with gauge and gravitational vertices and in the low-energy hydrodynamic regime lead to the chiral magnetic (CME) and chiral vortical effects (CVE) at non-zero chemical potential and temperature [1]}, [2]}, [3]}, [4]}: The CME is a chiral current along magnetic field at finite chemical potential(s), while the CVE involves a chiral current induced by hydrodynamic fluid flow with non-zero vorticity, e.g. the angular momentum of a rotating chiral system. Intuitively speaking, the CME is based on the analogy of (chiral) chemical potential with (chiral) temporal gauge fields, whereas the CVE rests in addition to the analogy of rotating frames to (tidal) gravitational forces.
